Sum of Different Primes

Time Limit: 5 Seconds
Memory Limit: 32768 KB

A positive integer may be expressed as a sum of different prime numbers
(primes), in one way or another. Given two positive integers *n* and
*k*, you should count the number of ways to express *n* as a sum
of *k* different primes. Here, two ways are considered to be the same
if they sum up the same set of the primes. For example, 8 can be expressed
as 3 + 5 and 5 + 3 but the are not distinguished.

When *n* and *k* are 24 and 3 respectively, the answer is two
because there are two sets {2, 3, 18} and {2, 5, 17} whose sums are equal
to 24. There are not other sets of three primes that sum up to 24. For
*n* = 24 and *k* = 2, the answer is three, because there are
three sets {5, 19}, {7, 17} and {11, 13}. For *n* = 2 and *k* =
1, the answer is one, because there is only one set {2} whose sum is 2.
For *n* = 1 and *k* = 1, the answer is zero. As 1 is not a
prime, you shouldn��t count {1}. For *n* = 4 and *k* = 2, the
answer is zero, because there are no sets of two different primes whose
sums are 4.

Your job is to write a program that reports the number of such ways for
the given *n* and *k*.

Input

The input is a sequence of datasets followed by a line containing two
zeros separated by a space. A dataset is a line containing two positive
integers *n* and *k* separated by a space. You may assume that
*n* �� 1120 and *k* �� 14.

Output

The output should be composed of lines, each corresponding to an input
dataset. An output line should contain one non-negative integer indicating
the number of the ways for *n* and *k* specified in the
corresponding dataset. You may assume that it is less than
2^{31}.

Sample Input

24 3
24 2
2 1
1 1
4 2
18 3
17 1
17 3
17 4
100 5
1000 10
1120 14
0 0

Sample Output

2
3
1
0
0
2
1
0
1
55
200102899
2079324314

Source:

**Asia Regional Contest, Yokohama, 2006**
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